Have you tried any gentler modifications to the push-up, i.e. a push-up at the wall?
Also, you mention that your client can do lots of shoulder and arm exercises, but you haven’t said anything about her strength and ability to fire the muscles in her chest. Have you tested her chest strength in other movements, such as a chest fly?
What I’ve done with beginners who couldn’t do push-ups on the floor, is started with resist-a-ball “presses,” where they hold a resist-a-ball straight out from their body, hands a little lower than shoulders, and then press in towards the center. That gives them an idea of whether their pectorals are firing and if they can “feel” their chest muscles. Then, I put them on a wall or a high bench or a bar on the weight rack and have them do a push-up on that incline, trying to get the same “feel” in their chest muscles as they did while doing the resist-a-ball press.